+1982 In parallelogram DEFG, the difference between two adjacent angles is 32 degrees. Which is the measure of the larger angle?
A. 96 degrees
B. 114 degrees
C. 106 degrees
D. 118 degrees
In a regular pentagon ABCDE and regular hexagon MNOPQR, 2AB = 3MN and CD + QR = 10. Which is 4BC + 5PQ?
A. 44
B. 33
C. 42
D. 38
+128475 First one
In a parallelogram, two adjacent angles sum to 180°
So
x + (x - 32) = 180
2x - 32 = 180 add 32 to both sides
2x = 212 divide both sides by 2
x = 106°
+128475 Let the side of the pentagon = x and the side of the hexagon = y
2AB = 3MN
CD + QR = 10 ......so.....
2x = 3y
x + y = 10
2x - 3y = 0
x + y = 10 multtiply the second equation by 3
2x - 3y = 0
3x + 3y = 30 add these
5x = 30
x = 6
And y = 4
So
4BC + 5PQ =
4(6) + 5(4) =
24 + 20 =
44
